Write the negation of each of the disjunction:
6 is greater than 4 or 6 is less than 9.

Answer

To find the negation of the disjunction "6 is greater than 4 or 6 is less than 9", we can follow these steps:

### Step 1: Identify the Statements
Let's define the two statements:
- Let \( P \): "6 is greater than 4"
- Let \( Q \): "6 is less than 9"

### Step 2: Write the Disjunction
The disjunction can be expressed as:
\[ P \lor Q \]
This means "P or Q", which translates to "6 is greater than 4 or 6 is less than 9".

### Step 3: Apply the Negation
To negate the disjunction \( P \lor Q \), we use De Morgan's Laws, which state:
\[ \neg (P \lor Q) = \neg P \land \neg Q \]
This means the negation of "P or Q" is equivalent to "not P and not Q".

### Step 4: Negate Each Statement
Now we need to find the negation of each statement:
- The negation of \( P \) ("6 is greater than 4") is:
\[ \neg P: 6 \text{ is not greater than } 4 \]
- The negation of \( Q \) ("6 is less than 9") is:
\[ \neg Q: 6 \text{ is not less than } 9 \]

### Step 5: Combine the Negations
Now we combine the negations using "and":
\[ \neg (P \lor Q) = \neg P \land \neg Q \]
This translates to:
"6 is not greater than 4 and 6 is not less than 9".

### Final Answer
Thus, the negation of the disjunction "6 is greater than 4 or 6 is less than 9" is:
**"6 is not greater than 4 and 6 is not less than 9."**

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